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Detailed kinetic and chemometric study of the cellulose thermal breakdown in artificially aged and non aged commercial paper. Different methods for computing activation energy as an assessment model in archaeometric applications
© Marini et al; licensee BioMed Central Ltd. 2012
- Published: 2 May 2012
The thermal oxidative degradation of aged and non aged cellulose samples of commercial paper was studied using thermogravimetry and derivative thermogravimetry under a forced air flow up to 800°C.
TG and DTG data were processed using two non-isothermal-based model-fitting methods and one based on linear least squares to calculate Ea trend values, measured as a function of artificially induced sample age. The Ea trends thus obtained were compared in order to assess their potential for yielding archaeometric curves. As the trends of first two methods show an inversion of the direction between non aged cellulose samples and artificially aged samples, while the third method does not, an in-depth study was carried out using a multilinearity assumption.
The results are discussed and the outcomes indicate that the above cited inversion is real and not linked to the method. Additionally, it was evidenced that the number of points used for the estimation of linear least squares model parameters is of capital importance.
- Paper Sample
- Multiple Linear Regression Method
- Thermal Breakdown
- Commercial Paper
It was postulated that in the paper or wood samples respectively aged naturally or artificially, the state of the cellulose polymer chains is damaged by well-known oxidative, photo-oxidative and hydrolytic processes, which occur during ageing . It was therefore attempted to correlate ageing, or the age, of the cellulosic samples with age-linked parameters that could be measured experimentally, if possible using relatively simple procedures and thus avoiding expensive apparatus [5–7].
In essence, it was endeavoured to detect any relationship between the breakdown of the cellulose and the physico–chemical parameters by which this could be evidenced. Consequently, the thermal oxidative degradation of non aged, or artificially aged, cellulose samples of commercial paper as such, or UV irradiated in a weatherometer, were studied using thermogravimetry (TG) and first-order derivative thermogravimetry (DTG) . In this framework the activation energy (Ea) values, which are related to cellulose fiber packing, seem to be more promising for the purpose of constructing archaeometric curves . However, there appears to be no recommended literature method for calculating the Ea of the cellulose thermal degradation process. Thus, in a previous study , in order to obtain reliable activation energy values and to identify the method yielding the most reliable data, a comparison was made between the results obtained by applying three different methods for calculating the Ea of the oxidative thermal breakdown of the cellulose contained in several different samples of aged and non aged paper. In particular, two non isothermal model-fitting methods – the differential Arrhenius [9, 11] and the integral Satava [9, 12] methods - were applied and the results obtained compared with those determined using the Wyden-Widmann method . All three methods are based on the linearization of suitable equations using the least squares method, from the slope of which the Ea values are determined. Nevertheless, a good correlation was found between Ea trends obtained using Arrhenius’ and Satava’s calculation methods and only partially with those obtained using Wyden-Widmann’s method.
The Ea trends obtained so far from TG/DTG data as a function of sample age for artificially aged extra-strong paper samples using the first two methods have not always been found to be completely linear. However, an inversion of the direction of these trends was found above all on going from fresh samples to aged samples, while the trends seem to be sufficiently linear whenever only samples of different artificial ageing times are considered.
For this purpose, from a previous study , it was found possible only to conclude that the cause of the inversion in the direction of the trend of Ea values observed in non aged cellulose samples, compared with aged samples, may be different and is often multiple in nature. For the time being it is not possible to conclude what the most plausible, or at least the most prevalent, reason might be that a degree of synergism possibly occurs also between several causes of this phenomenon. Furthermore, it must be determined to what extent the kinetic method used to calculate the Ea values actually affects the trends obtained. This point obviously calls for a more thorough investigation in order to to achieve full elucidation, which is precisely what has been attempted in the present note.
In the interpretation of these outcomes, it was not clear to what extent they depended on the real differences in the physico-chemical characteristics of the cellulose in the non aged sample versus the aged samples and, conversely, to what extent the kinetic method used to calculate the Ea values actually affected the Ea trends obtained using the equations (6, 7 and 9) for the Arrhenius, Satava and Wyden-Widmann methods, respectively. In the present research Wyden-Widmann’s method, which is very often applied automatically using computer implemented software coupled with the thermogravimetric apparatus, was thoroughly tested. Initially, computation of Wyden-Widmann model parameters was also tried using a non-least squares iterative method based on continuous-valued genetic algorithms  but results statistically comparable to those ones deriving from the application of the MLR method were obtained, both when applied to the linearized version and when nonlinear solution was evaluated directly. However, as also discussed in the Experimental section, we observed how the estimated value of Ea can change significantly depending on the temperature range (and, as a consequence, on the number of data points) selected for use in the fitting procedure. Accordingly, the computation of model parameters in the Wyden and Widmann method was repeated by including a different number of data points in the fitting procedure in order to account for this observation.
Model functions considered in this study along with their expressions.
First-order decay (n=1)
Second-order decay (n=2)
Third-order decay (n=3)
0.5 · (1– α)3
2 · (1– α) · [–ln(1– α)]0.5
Samples and apparatus
Paper ageing was achieved by photoirradiation at λ = 310 nm in a weatherometer (Model QUV/spray Q-Panel LAB-Products) for up to 750 hours. The apparatus was equipped with 8 mercury lamps (40 W each) able to simulate sunlight perfectly up to 370 nm.
Samples of extra-strong paper for photocopiers and laser printers (white paper for office photocopiers, Copy blu, Code 13092 - 6IN - format 21x29.7 cm, A4, basic weight 80 g m–2) were studied either as such or artificially aged in a weatherometer for different ageing periods up to a maximum of 750 h.
The TG/DTG measurements were carried out on a Mettler 50 thermobalance coupled with a Mettler TG 10-TA processor system and to a Swiss dot matrix printer.
For the purpose of performing thermogravimetric experiments, from each extra-strong paper sample 5 small circular disks (5.0±0.1 mm in diameter) were cut out, each weighing 1.7±0.1 mg. The diskettes were then placed in a special cylindrical alumina crucible, 0.7 cm in diameter, and carefully compressed using a small piston before being subjected to TG analysis under a forced air flow (0.1 dm3 min–1) at a heating rate of 10 °C min–1.
Another typical and well known commercially available Italian paper (“Fabriano” paper), both non aged or artificially aged in a weatherometer, was also analysed. In this case all the paper samples were minced finely before analysis. The size of individual paper fragments was of the order of 1.0 ± 0.2 mm2 on average.
In the course of artificial ageing in the weatherometer, Fabriano paper samples were taken at several irradiation times up to a maximum of 200 hours.
Determination of activation energy using the Arrhenius and Satava model-fitting procedure
In the two methods used, the left-hand side of equations (6) and (7) is assumed to be linear with respect to the reciprocal of the temperature (1/T) only for the functions f(α) and g(α) which represent the best mechanism for the reaction considered. From the slope and intercept of the regression straight lines described in equations (6) and (7) the values of the activation energy and the pre-exponential factor may be calculated. The differential and integral f(α) and g(α) functions that best fit the reaction mechanism were chosen from among those reported in literature  on the basis of experimental parameters referring to the shapes of DTG peaks related to the thermal oxidative process of cellulose contained in the wood or paper samples, as described in detail in previous papers [9, 22]. The model functions reported in literature  and selected in previous papers for similar cellulosic samples  are denoted by the symbols A (Avrami-Erofeev models) and F (nth-order decay models).
Determination of activation energy using the Wyden-Widmann method
where n is the order of reaction.
By applying the least squares method, the sum of the squares of the differences between the values of dα/dt calculated by equation (8) and those derived using TG/DTG measurements (taking into account that α is calculated using equation (2) and dα/dt = (dm/dt) /Δmtot where dm/dt is the rate of mass loss and Δmtot= mf–mi) attains its minimum value for given values of A, n and Ea, which are thereby identified. In particular, the value of the activation energy Ea is thus determined.
Further investigation: equation for multilinearity assumption
The left-hand side of equation (9) is linear with respect to both the reciprocal temperature and log(1-α). Therefore, it is customary for the values of the kinetic parameters to be computed following a multiple linear regression (MLR) approach. However, when the values of log(dα/dt), T and log(1-α) are obtained from the TG/DTG curves according to equation (9) and log(dα/dt) is plotted against (1/T) and log(1-α), not all the fitted data points are found to lie on the same plane, as is assumed in the same equation. Therefore, in order to obtain a reliable estimation of kinetic parameters, a suitable number of data points, sufficient to give an accurate fit but not so many as to include deviations from the linearity assumption, must be considered. Accordingly, in this investigation the effect of the number of data points to be used for computing model parameters in Wyden-Widmann’s approach on the quality of the final solution was also studied. This goal was obtained for each TG/DTG curve by computing MLR models based on an increasing number of data points from 21 to 201, symmetrically distributed around the temperature, corresponding to the minimum in DTG cellulose peak.
It may be concluded that: (i) the most correct Ea trend, as a function of the irradiation time in the weatherometer, seems to be the one obtained using the Satava and Arrhenius methods to identify the model function that best fits the experimental trend of the DTG peak values, (ii) A sufficiently correct trend may be obtained also by applying the Wyden–Widmann method but only using a suitable number of points right and left of the DTG peak, (iii) It is possible to choose the appropriate number of points in Wyden-Widmann’s approach by taking into account the multilinearity assumption and observing the temperature interval over which it is followed, (iv) It therefore seems that the inversion of trend found on going from the non aged extra-strong paper sample to the artificially aged samples is real and linked to the non aged paper sample and not to the method used to compute the Ea values, (iv) the choice of the best functional form (in the case of model fitting methods) and of the number of points to use for the computation of the regression parameters in the case of Wyden-Widmann’s method, is of capital importance for a correct final result.
Authors are indebted with Dr. C. Costanza and Prof. L. Campanella for making available the paper samples analysed which were artificially aged in a weatherometer. This work was funded by “Sapienza University of Rome”, Ateneo and University Projects.
This article has been published as part of Chemistry Central Journal Volume 6 Supplement 2, 2012: Proceedings of CMA4CH 2010: Application of Multivariate Analysis and Chemometry to Cultural Heritage and Environment. The full contents of the supplement are available online at http://journal.chemistrycentral.com/supplements/6/S2.
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